where \(||R|| = \mbox{Tr} \sqrt{R R^{\dagger }}\) , and the superscripts \(T_A\) , \(T_B\)  and \(T_C\) 
represent the partial transposes of \(\rho \)  with respect to the qubits \(A\) , \(B\)  and \(C\)  respectively.
Using the separability criterion based on partial transpose [1]}, [2]}, [3]},
it is easy to show that the global negativities vanish for separable states.
It is worthwhile noting that the computation of the global negativities is relatively simple
compared to the concurrence or three-tangle for mixed states since it does not need the convex-roof
extension defined in Eq. (REF ). In addition, the negativities also satisfy the monogamy inequality
\({\cal N}_{AB}^2 + {\cal N}_{AC}^2 \le {\cal N}_{A(BC)}^2\) 
